Stationary Incompressible Flow Research Articles

Local and Parallel Finite Element Algorithm Based on Oseen-Type Iteration for the Stationary Incompressible MHD Flow

In this work, we are concerned with the local and parallel finite element algorithm based on the Oseen-type iteration for solving the stationary incompressible magnetohydrodynamics. Under the uniqueness condition, the error estimates with respect to iterative step m and small mesh sizes H and $$h\ll H$$hźH of the proposed method are derived. Finally, some numerical experiments are provided to show the high efficiency of our algorithm.

Darcy’s Law for Flow in a Periodic Thin Porous Medium Confined Between Two Parallel Plates

We study stationary incompressible fluid flow in a thin periodic porous medium. The medium under consideration is a bounded perforated 3D-domain confined between two parallel plates. The distance b ...

A steady flow through a plane cascade of profiles with an arbitrarily large inflow_The mathematical model, existence of a weak solution

The paper deals with a mathematical model of a viscous stationary incompressible flow through a cascade of profiles. The problem for the Navier–Stokes system is formulated in a domain corresponding to one spatial period of the cascade. We consider several types of boundary conditions on various parts of the boundary (the inflow, the artificial lower and upper boundaries, the profile, the outflow). We solve the problem with an arbitrarily large inflow into the turbine. We formulate the “artificial” boundary condition on the outflow (the modification of the so called do-nothing condition) which enables us to prove the existence of a weak solution for any inflow.

Two-Scale Picard Stabilized Finite Volume Method for the Incompressible Flow

AbstractIn this paper, we consider a two-scale stabilized finite volume method for the two-dimensional stationary incompressible flow approximated by the lowest equal-order element pairP1—P1which do not satisfy the inf-sup condition. The two-scale method consist of solving a small non-linear system on the coarse mesh and then solving a linear Stokes equations on the fine mesh. Convergence of the optimal order in theH1-norm for velocity and theL2-norm for pressure are obtained. The error analysis shows there is the same convergence rate between the two-scale stabilized finite volume solution and the usual stabilized finite volume solution on a fine mesh with relationh = 𝾪(H2). Numerical experiments completely confirm theoretic results. Therefore, this method presented in this paper is of practical importance in scientific computation.

Linearized stationary incompressible flow around rotating and translating bodies -- Leray solutions

We consider Leray solutions of the Oseen system with rotational terms, in an exterior domain.Such solutions are characterized by square-integrability of the gradient of the velocityand local square-integrability of the pressure. In a previous paper, we had shown a pointwisedecay result for a slightly stronger type of solution. Here this result is extended toLeray solutions. We thus present a second access to this result, besides the onein G. P. Galdi, M. Kyed, Arch. Rat. Mech. Anal., 200 (2011), 21-58.

Twist parameter Influence on Heat Transfer Coefficient Augmentation for a square Twisted Tube

Heat transfer augmentation due to twisting parameter was investigated in atwisted tube of square cross sectional area. Twisting parameter is defined as the ratio of the length of the tube where it completed twisting of360 degrees to its hydraulic diameter. Four twist parameters were chosen;5, 10, 25 and 50, and a comparison is made with a straight untwisted duct. Two sets of Reynolds numbers were considered for laminar and transient flow. The laminar flow is performed at Re=500,1000,1500 and 2000. While for transient flow the range of Reynolds number are Re=5000,6000,7000,8000 and 9000.Theinfluence of twist parameter on convective heat transfer coefficient in laminar and transient flow was investigated. Numerical simulations were performed for three-dimensional, steady state incompressible flow in body-fitted coordinate using finite volume method and standard k-ε turbulence model. For the heat transfer problem the uniform wall temperature (UWT) boundary condition at tube wall is considered. It was observed that the heat transfer coefficient increases with decreasing twist parameter. This is interpreted to the nature of span wise swirling flow generated. The swirling increases cross flow velocity vectors as it becomes far from tube center towards walls. At tube wall the thickness of boundary layer becomes thinner as near wall velocity become larger which leads to a boundary layer of good thermal characteristics. Also swirling increases internal mixing process which enhances internal thermal equilibrium. The heat transfer coefficient also increases as Reynolds number increased as velocity components are increased

Stability of swirl flows with radial density gradient

The stability of an axially symmetrical stationary incompressible swirl flow with radial density jump in relation to infinitesimal spiral perturbations is investigated in the paper The dependences of perturbation frequency and increment on the swirl parameter, axial wave number and density jump are obtained. It is shown that perturbation frequency increases while its increment decreases with the increase in the medium density gradient.

An Adaptive Finite Element Method for Stationary Incompressible Thermal Flow Based on Projection Error Estimation

An adaptive finite element method is presented for the stationary incompressible thermal flow problems. A reliable a posteriori error estimator based on a projection operator is proposed and it can be computed easily and implemented in parallel. Finally, three numerical examples are given to illustrate the efficiency of the adaptive finite element method. We also show that the adaptive strategy is effective to detect local singularities in the physical model of square cavity stationary flow in the third example.

Velocity–pressure coupling on GPUs

We explore the possibilities to accelerate simulations in computational fluid dynamics by additional graphics processing units (GPUs). By examining some examples of stationary incompressible flows from the industrial practice we demon- strate that the potential speedup obtained by deploying GPU accelerated linear solvers alone is limited if standard segregated algorithms are used. However, recently pre- sented velocity-pressure coupling algorithms are an attractive alternative to these seg- regated algorithms. We present an efficient AMG solver for the coupled linear system of mixed elliptic-hyperbolic character and show that the GPU-accelerated version of this linear solver accelerates the velocity-pressure coupling scheme by almost 50 % compared to a competitive CPU implementation. Compared to standard segregated methods, the computing time of the whole simulation is reduced by up to 75 %.

Free Convective Heat Transfer in an Enclosure Filled with Porous Media with and without Insulated Moving Wall

The present work is concerned with the free convective two dimensional flow and heat transfer, in isotropic fluid filled porous rectangular enclosure with differentially heated walls for steady state incompressible flow have been investigated for non-Darcy flow model. Effects of Darcy number (0.0001  Da  10), Rayleigh number (10  Ra  5000), and aspect ratio (0.25  AR  4), for a range of porosity (0.4    0.9) with and without moving lower wall have been studied. The cavity was insulated at the lower and upper surfaces. The right and left heated surfaces allows convective transport through the porous medium, generating a thermal stratification and flow circulations. It was found that the Darcy number, Rayleigh number, aspect ratio, and porosity considerably influenced characteristics of flow and heat transfer mechanisms. The results obtained are discussed in terms of the Nusselt number, vectors, contours, and isotherms.

Complete classification of stationary flows with constant total pressure of ideal incompressible infinitely conducting fluid

The exhaustive classification of stationary incompressible flows with constant total pressure of ideal infinitely electrically conducting fluid is given. By introduction of curvilinear coordinates based on streamlines and magnetic lines of the flow, the system of magnetohydrodynamics equations is reduced to a nonlinear vector wave equation extended by the incompressibility condition in a form of a generalized Cauchy integral. For flows with constant total pressure, the wave equation is explicitly integrated, whereas the incompressibility condition is reduced to a scalar equation for functions, depending on different sets of variables. The central difficulty of the investigation is the separation of variables in the scalar equation, and integration of the resulting overdetermined systems of nonlinear partially differential equations. The canonical representatives of all possible types of solutions together with equivalence transformations that extend the canonical set to the whole amount of solutions are represented.

Monolithic Newton‐multigrid solution techniques for incompressible nonlinear flow models

SUMMARYWe present special Newton‐multigrid techniques for stationary incompressible nonlinear flow models discretized by the high order LBB‐stable Q2P1 element pair. We treat the resulting nonlinear and the corresponding linear discrete systems by a fully coupled monolithic approach to maintain high accuracy and robustness, particularly with respect to different rheological behaviors and also regarding different problem sizes and types of nonlinearity. Here, local pressure Schur complement techniques are presented as a generalization of the classical Vanka smoother. The discussed methodology is implemented for the well‐known flow around cylinder benchmark configuration for generalized Newtonian as well as non‐Newtonian flows including non‐isothermal, shear/pressure dependent and viscoelastic effects.Copyright © 2012 John Wiley & Sons, Ltd.

Linearized stationary incompressible flow around rotating and translating bodies: Asymptotic profile of the velocity gradient and decay estimate of the second derivatives of the velocity

We consider a system arising by linearization of a model for stationary viscous incompressible flow around a translating and rotating body. An asymptotic profile of the gradient of the velocity is derived. The leading term of the profile involves derivatives of a fundamental solution constructed by R.B. Guenther and E.A. Thomann (2006) [23], for the system in question. In addition, we establish decay estimates of the second derivatives of the velocity.

The meshless Galerkin boundary node method for Stokes problems in three dimensions

AbstractThe Galerkin boundary node method (GBNM) is a boundary only meshless method that combines an equivalent variational formulation of boundary integral equations for governing equations and the moving least‐squares (MLS) approximations for generating the trial and test functions. In this approach, boundary conditions can be implemented directly and easily despite of the fact that the MLS shape functions lack the delta function property. Besides, the resulting formulation inherits the symmetry and positive definiteness of the variational problems. The GBNM is developed in this paper for solving three‐dimensional stationary incompressible Stokes flows in primitive variables. The numerical scheme is based on variational formulations for the first‐kind integral equations, which are valid for both interior and exterior problems simultaneously. A rigorous error analysis and convergence study of the method for both the velocity and the pressure is presented in Sobolev spaces. The capability of the method is also illustrated and assessed through some selected numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.

A representation formula for linearized stationary incompressible viscous flows around rotating and translating bodies

A Green's formula is proved for solutions of a linearized system describing the stationary flow of a viscous incompressible fluid around a rigid body which is rotating and translating. The formula in question is based on the fundamental solution obtained by integrating the time variable in the fundamental solution of the corresponding evolutionary problem.

The alternating group explicit (AGE) iterative method for solving a Ladyzhenskaya model for stationary incompressible viscous flow

In this paper, the alternating group explicit (AGE) iterative method is applied to a nonlinear fourth-order PDE describing the flow of an incompressible fluid. This equation is a Ladyzhenskaya equation. The AGE method is shown to be extremely powerful and flexible and affords its users many advantages. Computational results are obtained to demonstrate the applicability of the method on some problems with known solutions. This paper demonstrates that the AGE method can be implemented to approximate solutions efficiently to the Navier–Stokes equations and the Ladyzhenskaya equations. Problems with a known solution are considered to test the method and to compare the computed results with the exact values. Streamfunction contours and some plots are displayed showing the main features of the solution.

Stability of a finite element method for 3D exterior stationary Navier-Stokes flows

We consider numerical approximations of stationary incompressible Navier-Stokes flows in 3D exterior domains, with nonzero velocity at infinity. It is shown that a P1-P1 stabilized finite element method proposed by C. Rebollo: A term by term stabilization algorithm for finite element solution of incompressible flow problems, Numer. Math. 79 (1998), 283–319, is stable when applied to a Navier-Stokes flow in a truncated exterior domain with a pointwise boundary condition on the artificial boundary.

Discontinuous Galerkin finite element approximation of the two‐dimensional Navier–Stokes equations in stream‐function formulation

AbstractIn this paper, we present the construction and computational assessment of an hp‐version discontinuous Galerkin finite element method (DGFEM) for the numerical solution of the Navier–Stokes equations governing 2D stationary incompressible flows. Using a stream‐function formulation, which ensures that the incompressibility constraint is automatically satisfied, we reduce the system of Navier–Stokes equations to a single fourth‐order nonlinear partial differential equation. We introduce a discretization of this fourth‐order nonlinear partial differential equation based on a combination of the symmetric DGFEM for the biharmonic part of the equation and a DGFEM with jump‐penalty terms for the hyperbolic part of the problem, and then we solve the resulting nonlinear problem using Newton's method. Numerical examples, including the solution of the 2D lid‐driven cavity flow problem, are presented to demonstrate the convergence and accuracy of the method. Copyright © 2006 John Wiley & Sons, Ltd.

Non-Riemannian geometry of twisted flux tubes

New examples of the theory recently proposed by Ricca [PRA(1991)] on the generalization of Da Rios-Betchov intrinsic equations on curvature and torsion of classical non-Riemannian vortex higher-dimensional string are given. In particular we consider applications to 3-dimesional fluid dynamics, including the case of a twisted flux tube and the fluid rotation. In this case use is made of Da Rios equation to constrain the fluid. Integrals on the Cartan connection are shown to be related to the integrals which represent the total Frenet torsion and total curvature. By analogy with the blue phases twisted tubes in liquid crystals, non-Riemannian geometrical formulation of the twisted flux tube in fluid dynamics is obtained. A theorem by Ricca and Moffatt on invariant integrals for the Frenet curvature is used to place limits on the Cartan integrals. The stationary incompressible flow case is also addressed in the non-Riemannian case where Cartan torsion scalars are shown to correspond to abnormalities of the congruence. Geodesic motion is shown to be torsionless. Vorticity is shown to be expressed in terms of abnormalities of the congruence, which is analogous to the result recenly obtained [Garcia de Andrade,PRD(2004)], where the vorticity of the superfluid plays the role of Cartan contortion vector in the context of analog gravity.

Reaction-Convection in Incompressible 3D-Fluid: A Homogenization Problem

We consider reaction-convection in a stationary incompressible flow which is close to a planar motion. Under certain conditions, we introduce the notion of relative entropy for such a deterministic flow to describe the motion of the spot occupied by an ingredient.